1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 141,297 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  2 111       2020-03-18 fema… 0-18  e380000… nhs_bed…    27 mk454hr  East of E…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_bla…     9 bb12fd   North West
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_bro…    11 br33ql   London    
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_can…     9 ws111jp  Midlands  
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_cit…    12 n15lz    London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_enf…     7 en40dy   London    
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_ham…     6 dl62uu   North Eas…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_har…    24 ts232la  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_kin…     6 kt11eu   London    
## # … with 141,287 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     62
## 33   2020-04-02          East of England     64
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     91
## 43   2020-04-12          East of England    101
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     45
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     36
## 67   2020-05-06          East of England     30
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     25
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     16
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     15
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     17
## 94   2020-06-02          East of England     14
## 95   2020-06-03          East of England      9
## 96   2020-06-04          East of England      7
## 97   2020-06-05          East of England     12
## 98   2020-06-06          East of England      4
## 99   2020-06-07          East of England      9
## 100  2020-06-08          East of England      5
## 101  2020-06-09          East of England      4
## 102  2020-06-10          East of England      1
## 103  2020-03-01                   London      0
## 104  2020-03-02                   London      0
## 105  2020-03-03                   London      0
## 106  2020-03-04                   London      0
## 107  2020-03-05                   London      0
## 108  2020-03-06                   London      1
## 109  2020-03-07                   London      1
## 110  2020-03-08                   London      0
## 111  2020-03-09                   London      1
## 112  2020-03-10                   London      0
## 113  2020-03-11                   London      7
## 114  2020-03-12                   London      6
## 115  2020-03-13                   London     10
## 116  2020-03-14                   London     14
## 117  2020-03-15                   London     10
## 118  2020-03-16                   London     17
## 119  2020-03-17                   London     25
## 120  2020-03-18                   London     31
## 121  2020-03-19                   London     25
## 122  2020-03-20                   London     45
## 123  2020-03-21                   London     50
## 124  2020-03-22                   London     54
## 125  2020-03-23                   London     64
## 126  2020-03-24                   London     87
## 127  2020-03-25                   London    113
## 128  2020-03-26                   London    130
## 129  2020-03-27                   London    130
## 130  2020-03-28                   London    122
## 131  2020-03-29                   London    147
## 132  2020-03-30                   London    150
## 133  2020-03-31                   London    181
## 134  2020-04-01                   London    202
## 135  2020-04-02                   London    190
## 136  2020-04-03                   London    196
## 137  2020-04-04                   London    230
## 138  2020-04-05                   London    195
## 139  2020-04-06                   London    198
## 140  2020-04-07                   London    219
## 141  2020-04-08                   London    238
## 142  2020-04-09                   London    206
## 143  2020-04-10                   London    170
## 144  2020-04-11                   London    177
## 145  2020-04-12                   London    158
## 146  2020-04-13                   London    166
## 147  2020-04-14                   London    144
## 148  2020-04-15                   London    142
## 149  2020-04-16                   London    139
## 150  2020-04-17                   London    100
## 151  2020-04-18                   London    101
## 152  2020-04-19                   London    103
## 153  2020-04-20                   London     95
## 154  2020-04-21                   London     95
## 155  2020-04-22                   London    108
## 156  2020-04-23                   London     77
## 157  2020-04-24                   London     71
## 158  2020-04-25                   London     58
## 159  2020-04-26                   London     53
## 160  2020-04-27                   London     51
## 161  2020-04-28                   London     43
## 162  2020-04-29                   London     44
## 163  2020-04-30                   London     40
## 164  2020-05-01                   London     41
## 165  2020-05-02                   London     40
## 166  2020-05-03                   London     36
## 167  2020-05-04                   London     30
## 168  2020-05-05                   London     25
## 169  2020-05-06                   London     37
## 170  2020-05-07                   London     37
## 171  2020-05-08                   London     29
## 172  2020-05-09                   London     23
## 173  2020-05-10                   London     26
## 174  2020-05-11                   London     18
## 175  2020-05-12                   London     18
## 176  2020-05-13                   London     16
## 177  2020-05-14                   London     20
## 178  2020-05-15                   London     18
## 179  2020-05-16                   London     14
## 180  2020-05-17                   London     15
## 181  2020-05-18                   London      9
## 182  2020-05-19                   London     13
## 183  2020-05-20                   London     19
## 184  2020-05-21                   London     12
## 185  2020-05-22                   London     10
## 186  2020-05-23                   London      6
## 187  2020-05-24                   London      7
## 188  2020-05-25                   London      9
## 189  2020-05-26                   London     12
## 190  2020-05-27                   London      7
## 191  2020-05-28                   London      8
## 192  2020-05-29                   London      7
## 193  2020-05-30                   London     12
## 194  2020-05-31                   London      6
## 195  2020-06-01                   London      9
## 196  2020-06-02                   London      7
## 197  2020-06-03                   London      5
## 198  2020-06-04                   London      8
## 199  2020-06-05                   London      3
## 200  2020-06-06                   London      0
## 201  2020-06-07                   London      4
## 202  2020-06-08                   London      5
## 203  2020-06-09                   London      1
## 204  2020-06-10                   London      1
## 205  2020-03-01                 Midlands      0
## 206  2020-03-02                 Midlands      0
## 207  2020-03-03                 Midlands      1
## 208  2020-03-04                 Midlands      0
## 209  2020-03-05                 Midlands      0
## 210  2020-03-06                 Midlands      0
## 211  2020-03-07                 Midlands      0
## 212  2020-03-08                 Midlands      3
## 213  2020-03-09                 Midlands      1
## 214  2020-03-10                 Midlands      0
## 215  2020-03-11                 Midlands      2
## 216  2020-03-12                 Midlands      6
## 217  2020-03-13                 Midlands      5
## 218  2020-03-14                 Midlands      4
## 219  2020-03-15                 Midlands      5
## 220  2020-03-16                 Midlands     11
## 221  2020-03-17                 Midlands      8
## 222  2020-03-18                 Midlands     13
## 223  2020-03-19                 Midlands      8
## 224  2020-03-20                 Midlands     28
## 225  2020-03-21                 Midlands     13
## 226  2020-03-22                 Midlands     31
## 227  2020-03-23                 Midlands     33
## 228  2020-03-24                 Midlands     41
## 229  2020-03-25                 Midlands     48
## 230  2020-03-26                 Midlands     64
## 231  2020-03-27                 Midlands     72
## 232  2020-03-28                 Midlands     89
## 233  2020-03-29                 Midlands     92
## 234  2020-03-30                 Midlands     90
## 235  2020-03-31                 Midlands    123
## 236  2020-04-01                 Midlands    140
## 237  2020-04-02                 Midlands    142
## 238  2020-04-03                 Midlands    124
## 239  2020-04-04                 Midlands    151
## 240  2020-04-05                 Midlands    164
## 241  2020-04-06                 Midlands    140
## 242  2020-04-07                 Midlands    123
## 243  2020-04-08                 Midlands    186
## 244  2020-04-09                 Midlands    139
## 245  2020-04-10                 Midlands    127
## 246  2020-04-11                 Midlands    142
## 247  2020-04-12                 Midlands    139
## 248  2020-04-13                 Midlands    120
## 249  2020-04-14                 Midlands    116
## 250  2020-04-15                 Midlands    147
## 251  2020-04-16                 Midlands    102
## 252  2020-04-17                 Midlands    118
## 253  2020-04-18                 Midlands    115
## 254  2020-04-19                 Midlands     92
## 255  2020-04-20                 Midlands    107
## 256  2020-04-21                 Midlands     86
## 257  2020-04-22                 Midlands     78
## 258  2020-04-23                 Midlands    103
## 259  2020-04-24                 Midlands     79
## 260  2020-04-25                 Midlands     72
## 261  2020-04-26                 Midlands     81
## 262  2020-04-27                 Midlands     74
## 263  2020-04-28                 Midlands     68
## 264  2020-04-29                 Midlands     53
## 265  2020-04-30                 Midlands     56
## 266  2020-05-01                 Midlands     64
## 267  2020-05-02                 Midlands     51
## 268  2020-05-03                 Midlands     52
## 269  2020-05-04                 Midlands     61
## 270  2020-05-05                 Midlands     58
## 271  2020-05-06                 Midlands     59
## 272  2020-05-07                 Midlands     48
## 273  2020-05-08                 Midlands     34
## 274  2020-05-09                 Midlands     37
## 275  2020-05-10                 Midlands     42
## 276  2020-05-11                 Midlands     33
## 277  2020-05-12                 Midlands     45
## 278  2020-05-13                 Midlands     39
## 279  2020-05-14                 Midlands     37
## 280  2020-05-15                 Midlands     40
## 281  2020-05-16                 Midlands     34
## 282  2020-05-17                 Midlands     31
## 283  2020-05-18                 Midlands     34
## 284  2020-05-19                 Midlands     34
## 285  2020-05-20                 Midlands     36
## 286  2020-05-21                 Midlands     32
## 287  2020-05-22                 Midlands     27
## 288  2020-05-23                 Midlands     34
## 289  2020-05-24                 Midlands     19
## 290  2020-05-25                 Midlands     26
## 291  2020-05-26                 Midlands     33
## 292  2020-05-27                 Midlands     29
## 293  2020-05-28                 Midlands     27
## 294  2020-05-29                 Midlands     20
## 295  2020-05-30                 Midlands     20
## 296  2020-05-31                 Midlands     21
## 297  2020-06-01                 Midlands     20
## 298  2020-06-02                 Midlands     21
## 299  2020-06-03                 Midlands     23
## 300  2020-06-04                 Midlands     15
## 301  2020-06-05                 Midlands     21
## 302  2020-06-06                 Midlands     19
## 303  2020-06-07                 Midlands     14
## 304  2020-06-08                 Midlands     14
## 305  2020-06-09                 Midlands     14
## 306  2020-06-10                 Midlands      3
## 307  2020-03-01 North East and Yorkshire      0
## 308  2020-03-02 North East and Yorkshire      0
## 309  2020-03-03 North East and Yorkshire      0
## 310  2020-03-04 North East and Yorkshire      0
## 311  2020-03-05 North East and Yorkshire      0
## 312  2020-03-06 North East and Yorkshire      0
## 313  2020-03-07 North East and Yorkshire      0
## 314  2020-03-08 North East and Yorkshire      0
## 315  2020-03-09 North East and Yorkshire      0
## 316  2020-03-10 North East and Yorkshire      0
## 317  2020-03-11 North East and Yorkshire      0
## 318  2020-03-12 North East and Yorkshire      0
## 319  2020-03-13 North East and Yorkshire      0
## 320  2020-03-14 North East and Yorkshire      0
## 321  2020-03-15 North East and Yorkshire      2
## 322  2020-03-16 North East and Yorkshire      3
## 323  2020-03-17 North East and Yorkshire      1
## 324  2020-03-18 North East and Yorkshire      2
## 325  2020-03-19 North East and Yorkshire      6
## 326  2020-03-20 North East and Yorkshire      5
## 327  2020-03-21 North East and Yorkshire      6
## 328  2020-03-22 North East and Yorkshire      7
## 329  2020-03-23 North East and Yorkshire      9
## 330  2020-03-24 North East and Yorkshire      8
## 331  2020-03-25 North East and Yorkshire     18
## 332  2020-03-26 North East and Yorkshire     21
## 333  2020-03-27 North East and Yorkshire     28
## 334  2020-03-28 North East and Yorkshire     35
## 335  2020-03-29 North East and Yorkshire     38
## 336  2020-03-30 North East and Yorkshire     64
## 337  2020-03-31 North East and Yorkshire     60
## 338  2020-04-01 North East and Yorkshire     67
## 339  2020-04-02 North East and Yorkshire     74
## 340  2020-04-03 North East and Yorkshire    100
## 341  2020-04-04 North East and Yorkshire    105
## 342  2020-04-05 North East and Yorkshire     92
## 343  2020-04-06 North East and Yorkshire     96
## 344  2020-04-07 North East and Yorkshire    102
## 345  2020-04-08 North East and Yorkshire    107
## 346  2020-04-09 North East and Yorkshire    111
## 347  2020-04-10 North East and Yorkshire    117
## 348  2020-04-11 North East and Yorkshire     98
## 349  2020-04-12 North East and Yorkshire     84
## 350  2020-04-13 North East and Yorkshire     94
## 351  2020-04-14 North East and Yorkshire    107
## 352  2020-04-15 North East and Yorkshire     96
## 353  2020-04-16 North East and Yorkshire    103
## 354  2020-04-17 North East and Yorkshire     88
## 355  2020-04-18 North East and Yorkshire     95
## 356  2020-04-19 North East and Yorkshire     88
## 357  2020-04-20 North East and Yorkshire    100
## 358  2020-04-21 North East and Yorkshire     76
## 359  2020-04-22 North East and Yorkshire     84
## 360  2020-04-23 North East and Yorkshire     63
## 361  2020-04-24 North East and Yorkshire     72
## 362  2020-04-25 North East and Yorkshire     69
## 363  2020-04-26 North East and Yorkshire     65
## 364  2020-04-27 North East and Yorkshire     65
## 365  2020-04-28 North East and Yorkshire     57
## 366  2020-04-29 North East and Yorkshire     69
## 367  2020-04-30 North East and Yorkshire     57
## 368  2020-05-01 North East and Yorkshire     64
## 369  2020-05-02 North East and Yorkshire     48
## 370  2020-05-03 North East and Yorkshire     40
## 371  2020-05-04 North East and Yorkshire     49
## 372  2020-05-05 North East and Yorkshire     40
## 373  2020-05-06 North East and Yorkshire     50
## 374  2020-05-07 North East and Yorkshire     45
## 375  2020-05-08 North East and Yorkshire     42
## 376  2020-05-09 North East and Yorkshire     44
## 377  2020-05-10 North East and Yorkshire     40
## 378  2020-05-11 North East and Yorkshire     29
## 379  2020-05-12 North East and Yorkshire     27
## 380  2020-05-13 North East and Yorkshire     28
## 381  2020-05-14 North East and Yorkshire     30
## 382  2020-05-15 North East and Yorkshire     32
## 383  2020-05-16 North East and Yorkshire     35
## 384  2020-05-17 North East and Yorkshire     26
## 385  2020-05-18 North East and Yorkshire     29
## 386  2020-05-19 North East and Yorkshire     27
## 387  2020-05-20 North East and Yorkshire     21
## 388  2020-05-21 North East and Yorkshire     33
## 389  2020-05-22 North East and Yorkshire     22
## 390  2020-05-23 North East and Yorkshire     18
## 391  2020-05-24 North East and Yorkshire     25
## 392  2020-05-25 North East and Yorkshire     21
## 393  2020-05-26 North East and Yorkshire     21
## 394  2020-05-27 North East and Yorkshire     21
## 395  2020-05-28 North East and Yorkshire     19
## 396  2020-05-29 North East and Yorkshire     24
## 397  2020-05-30 North East and Yorkshire     20
## 398  2020-05-31 North East and Yorkshire     19
## 399  2020-06-01 North East and Yorkshire     16
## 400  2020-06-02 North East and Yorkshire     22
## 401  2020-06-03 North East and Yorkshire     22
## 402  2020-06-04 North East and Yorkshire     17
## 403  2020-06-05 North East and Yorkshire     17
## 404  2020-06-06 North East and Yorkshire     20
## 405  2020-06-07 North East and Yorkshire     12
## 406  2020-06-08 North East and Yorkshire     11
## 407  2020-06-09 North East and Yorkshire     10
## 408  2020-06-10 North East and Yorkshire      7
## 409  2020-03-01               North West      0
## 410  2020-03-02               North West      0
## 411  2020-03-03               North West      0
## 412  2020-03-04               North West      0
## 413  2020-03-05               North West      1
## 414  2020-03-06               North West      0
## 415  2020-03-07               North West      0
## 416  2020-03-08               North West      1
## 417  2020-03-09               North West      0
## 418  2020-03-10               North West      0
## 419  2020-03-11               North West      0
## 420  2020-03-12               North West      2
## 421  2020-03-13               North West      3
## 422  2020-03-14               North West      1
## 423  2020-03-15               North West      4
## 424  2020-03-16               North West      2
## 425  2020-03-17               North West      4
## 426  2020-03-18               North West      6
## 427  2020-03-19               North West      7
## 428  2020-03-20               North West     10
## 429  2020-03-21               North West     11
## 430  2020-03-22               North West     13
## 431  2020-03-23               North West     16
## 432  2020-03-24               North West     21
## 433  2020-03-25               North West     21
## 434  2020-03-26               North West     29
## 435  2020-03-27               North West     35
## 436  2020-03-28               North West     28
## 437  2020-03-29               North West     46
## 438  2020-03-30               North West     67
## 439  2020-03-31               North West     52
## 440  2020-04-01               North West     86
## 441  2020-04-02               North West     96
## 442  2020-04-03               North West     95
## 443  2020-04-04               North West     98
## 444  2020-04-05               North West    102
## 445  2020-04-06               North West    100
## 446  2020-04-07               North West    134
## 447  2020-04-08               North West    127
## 448  2020-04-09               North West    119
## 449  2020-04-10               North West    117
## 450  2020-04-11               North West    138
## 451  2020-04-12               North West    126
## 452  2020-04-13               North West    129
## 453  2020-04-14               North West    131
## 454  2020-04-15               North West    114
## 455  2020-04-16               North West    134
## 456  2020-04-17               North West     98
## 457  2020-04-18               North West    113
## 458  2020-04-19               North West     71
## 459  2020-04-20               North West     83
## 460  2020-04-21               North West     76
## 461  2020-04-22               North West     86
## 462  2020-04-23               North West     85
## 463  2020-04-24               North West     66
## 464  2020-04-25               North West     65
## 465  2020-04-26               North West     55
## 466  2020-04-27               North West     54
## 467  2020-04-28               North West     57
## 468  2020-04-29               North West     62
## 469  2020-04-30               North West     59
## 470  2020-05-01               North West     44
## 471  2020-05-02               North West     56
## 472  2020-05-03               North West     55
## 473  2020-05-04               North West     48
## 474  2020-05-05               North West     48
## 475  2020-05-06               North West     44
## 476  2020-05-07               North West     49
## 477  2020-05-08               North West     42
## 478  2020-05-09               North West     30
## 479  2020-05-10               North West     41
## 480  2020-05-11               North West     34
## 481  2020-05-12               North West     38
## 482  2020-05-13               North West     24
## 483  2020-05-14               North West     26
## 484  2020-05-15               North West     33
## 485  2020-05-16               North West     32
## 486  2020-05-17               North West     24
## 487  2020-05-18               North West     31
## 488  2020-05-19               North West     35
## 489  2020-05-20               North West     27
## 490  2020-05-21               North West     26
## 491  2020-05-22               North West     26
## 492  2020-05-23               North West     31
## 493  2020-05-24               North West     26
## 494  2020-05-25               North West     31
## 495  2020-05-26               North West     27
## 496  2020-05-27               North West     27
## 497  2020-05-28               North West     28
## 498  2020-05-29               North West     19
## 499  2020-05-30               North West     17
## 500  2020-05-31               North West     13
## 501  2020-06-01               North West     12
## 502  2020-06-02               North West     26
## 503  2020-06-03               North West     21
## 504  2020-06-04               North West     19
## 505  2020-06-05               North West     15
## 506  2020-06-06               North West     20
## 507  2020-06-07               North West     17
## 508  2020-06-08               North West     17
## 509  2020-06-09               North West      7
## 510  2020-06-10               North West      0
## 511  2020-03-01               South East      0
## 512  2020-03-02               South East      0
## 513  2020-03-03               South East      1
## 514  2020-03-04               South East      0
## 515  2020-03-05               South East      1
## 516  2020-03-06               South East      0
## 517  2020-03-07               South East      0
## 518  2020-03-08               South East      1
## 519  2020-03-09               South East      1
## 520  2020-03-10               South East      1
## 521  2020-03-11               South East      1
## 522  2020-03-12               South East      0
## 523  2020-03-13               South East      1
## 524  2020-03-14               South East      1
## 525  2020-03-15               South East      5
## 526  2020-03-16               South East      8
## 527  2020-03-17               South East      7
## 528  2020-03-18               South East     10
## 529  2020-03-19               South East      9
## 530  2020-03-20               South East     14
## 531  2020-03-21               South East      7
## 532  2020-03-22               South East     25
## 533  2020-03-23               South East     20
## 534  2020-03-24               South East     22
## 535  2020-03-25               South East     29
## 536  2020-03-26               South East     34
## 537  2020-03-27               South East     34
## 538  2020-03-28               South East     36
## 539  2020-03-29               South East     54
## 540  2020-03-30               South East     58
## 541  2020-03-31               South East     65
## 542  2020-04-01               South East     66
## 543  2020-04-02               South East     55
## 544  2020-04-03               South East     72
## 545  2020-04-04               South East     80
## 546  2020-04-05               South East     82
## 547  2020-04-06               South East     88
## 548  2020-04-07               South East    100
## 549  2020-04-08               South East     83
## 550  2020-04-09               South East    104
## 551  2020-04-10               South East     88
## 552  2020-04-11               South East     88
## 553  2020-04-12               South East     88
## 554  2020-04-13               South East     84
## 555  2020-04-14               South East     65
## 556  2020-04-15               South East     72
## 557  2020-04-16               South East     56
## 558  2020-04-17               South East     86
## 559  2020-04-18               South East     57
## 560  2020-04-19               South East     70
## 561  2020-04-20               South East     85
## 562  2020-04-21               South East     50
## 563  2020-04-22               South East     54
## 564  2020-04-23               South East     57
## 565  2020-04-24               South East     64
## 566  2020-04-25               South East     51
## 567  2020-04-26               South East     51
## 568  2020-04-27               South East     40
## 569  2020-04-28               South East     40
## 570  2020-04-29               South East     47
## 571  2020-04-30               South East     29
## 572  2020-05-01               South East     37
## 573  2020-05-02               South East     36
## 574  2020-05-03               South East     17
## 575  2020-05-04               South East     35
## 576  2020-05-05               South East     29
## 577  2020-05-06               South East     25
## 578  2020-05-07               South East     27
## 579  2020-05-08               South East     26
## 580  2020-05-09               South East     28
## 581  2020-05-10               South East     19
## 582  2020-05-11               South East     25
## 583  2020-05-12               South East     27
## 584  2020-05-13               South East     18
## 585  2020-05-14               South East     32
## 586  2020-05-15               South East     24
## 587  2020-05-16               South East     22
## 588  2020-05-17               South East     18
## 589  2020-05-18               South East     22
## 590  2020-05-19               South East     12
## 591  2020-05-20               South East     22
## 592  2020-05-21               South East     14
## 593  2020-05-22               South East     17
## 594  2020-05-23               South East     21
## 595  2020-05-24               South East     16
## 596  2020-05-25               South East     13
## 597  2020-05-26               South East     19
## 598  2020-05-27               South East     17
## 599  2020-05-28               South East     12
## 600  2020-05-29               South East     17
## 601  2020-05-30               South East      8
## 602  2020-05-31               South East     10
## 603  2020-06-01               South East     11
## 604  2020-06-02               South East     12
## 605  2020-06-03               South East     17
## 606  2020-06-04               South East     11
## 607  2020-06-05               South East      9
## 608  2020-06-06               South East      9
## 609  2020-06-07               South East     10
## 610  2020-06-08               South East      5
## 611  2020-06-09               South East      6
## 612  2020-06-10               South East      1
## 613  2020-03-01               South West      0
## 614  2020-03-02               South West      0
## 615  2020-03-03               South West      0
## 616  2020-03-04               South West      0
## 617  2020-03-05               South West      0
## 618  2020-03-06               South West      0
## 619  2020-03-07               South West      0
## 620  2020-03-08               South West      0
## 621  2020-03-09               South West      0
## 622  2020-03-10               South West      0
## 623  2020-03-11               South West      1
## 624  2020-03-12               South West      0
## 625  2020-03-13               South West      0
## 626  2020-03-14               South West      1
## 627  2020-03-15               South West      0
## 628  2020-03-16               South West      0
## 629  2020-03-17               South West      2
## 630  2020-03-18               South West      2
## 631  2020-03-19               South West      5
## 632  2020-03-20               South West      3
## 633  2020-03-21               South West      6
## 634  2020-03-22               South West      9
## 635  2020-03-23               South West      9
## 636  2020-03-24               South West      7
## 637  2020-03-25               South West      9
## 638  2020-03-26               South West     11
## 639  2020-03-27               South West     13
## 640  2020-03-28               South West     21
## 641  2020-03-29               South West     18
## 642  2020-03-30               South West     23
## 643  2020-03-31               South West     23
## 644  2020-04-01               South West     22
## 645  2020-04-02               South West     23
## 646  2020-04-03               South West     30
## 647  2020-04-04               South West     42
## 648  2020-04-05               South West     32
## 649  2020-04-06               South West     34
## 650  2020-04-07               South West     39
## 651  2020-04-08               South West     47
## 652  2020-04-09               South West     24
## 653  2020-04-10               South West     46
## 654  2020-04-11               South West     43
## 655  2020-04-12               South West     23
## 656  2020-04-13               South West     27
## 657  2020-04-14               South West     24
## 658  2020-04-15               South West     32
## 659  2020-04-16               South West     29
## 660  2020-04-17               South West     33
## 661  2020-04-18               South West     25
## 662  2020-04-19               South West     31
## 663  2020-04-20               South West     26
## 664  2020-04-21               South West     26
## 665  2020-04-22               South West     23
## 666  2020-04-23               South West     17
## 667  2020-04-24               South West     19
## 668  2020-04-25               South West     15
## 669  2020-04-26               South West     27
## 670  2020-04-27               South West     13
## 671  2020-04-28               South West     17
## 672  2020-04-29               South West     15
## 673  2020-04-30               South West     26
## 674  2020-05-01               South West      6
## 675  2020-05-02               South West      7
## 676  2020-05-03               South West     10
## 677  2020-05-04               South West     16
## 678  2020-05-05               South West     14
## 679  2020-05-06               South West     19
## 680  2020-05-07               South West     16
## 681  2020-05-08               South West      6
## 682  2020-05-09               South West     11
## 683  2020-05-10               South West      5
## 684  2020-05-11               South West      8
## 685  2020-05-12               South West      7
## 686  2020-05-13               South West      7
## 687  2020-05-14               South West      6
## 688  2020-05-15               South West      4
## 689  2020-05-16               South West      4
## 690  2020-05-17               South West      6
## 691  2020-05-18               South West      4
## 692  2020-05-19               South West      6
## 693  2020-05-20               South West      1
## 694  2020-05-21               South West      9
## 695  2020-05-22               South West      6
## 696  2020-05-23               South West      6
## 697  2020-05-24               South West      3
## 698  2020-05-25               South West      8
## 699  2020-05-26               South West     11
## 700  2020-05-27               South West      5
## 701  2020-05-28               South West      9
## 702  2020-05-29               South West      4
## 703  2020-05-30               South West      3
## 704  2020-05-31               South West      2
## 705  2020-06-01               South West      6
## 706  2020-06-02               South West      2
## 707  2020-06-03               South West      5
## 708  2020-06-04               South West      2
## 709  2020-06-05               South West      1
## 710  2020-06-06               South West      1
## 711  2020-06-07               South West      2
## 712  2020-06-08               South West      2
## 713  2020-06-09               South West      0
## 714  2020-06-10               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-06-10"

The completion date of the NHS Pathways data is Wednesday 10 Jun 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -8.2487  -2.1739  -0.4845   1.9436   4.5033  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 5.066e+00  5.076e-02   99.79   <2e-16 ***
## note_lag    1.067e-05  4.933e-07   21.63   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 8.248572)
## 
##     Null deviance: 4173.18  on 40  degrees of freedom
## Residual deviance:  330.29  on 39  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  158.463488    1.000011
exp(confint(lag_mod))
##                 2.5 %     97.5 %
## (Intercept) 143.31427 174.871010
## note_lag      1.00001   1.000012

Rsq(lag_mod)
## [1] 0.9208532

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Tue May 26 20:41:44 PDT 2020; root:xnu-6153.121.2~2/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1467.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin15.6.0   
## arch           x86_64                      
## os             darwin15.6.0                
## system         x86_64, darwin15.6.0        
## status                                     
## major          3                           
## minor          6.3                         
## year           2020                        
## month          02                          
## day            29                          
## svn rev        77875                       
## language       R                           
## version.string R version 3.6.3 (2020-02-29)
## nickname       Holding the Windsock

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.3.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.13             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.4.1    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.1         ggplot2_3.3.1       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] colorspace_1.4-1  selectr_0.4-2     ggsignif_0.6.0    ellipsis_0.3.1   
##  [5] rprojroot_1.3-2   snakecase_0.11.0  fs_1.4.1          rstudioapi_0.11  
##  [9] farver_2.0.3      fansi_0.4.1       splines_3.6.3     knitr_1.28       
## [13] jsonlite_1.6.1    broom_0.5.6       dbplyr_1.4.4      compiler_3.6.3   
## [17] httr_1.4.1        backports_1.1.7   assertthat_0.2.1  Matrix_1.2-18    
## [21] cli_2.0.2         htmltools_0.4.0   prettyunits_1.1.1 tools_3.6.3      
## [25] gtable_0.3.0      glue_1.4.1        Rcpp_1.0.4.6      carData_3.0-4    
## [29] cellranger_1.1.0  vctrs_0.3.1       nlme_3.1-144      matchmaker_0.1.1 
## [33] crosstalk_1.1.0.1 xfun_0.14         ps_1.3.3          openxlsx_4.1.5   
## [37] lifecycle_0.2.0   rstatix_0.5.0     MASS_7.3-51.5     scales_1.1.1     
## [41] hms_0.5.3         sodium_1.1        yaml_2.2.1        curl_4.3         
## [45] gridExtra_2.3     stringi_1.4.6     kyotil_2019.11-22 boot_1.3-24      
## [49] pkgbuild_1.0.8    zip_2.0.4         rlang_0.4.6       pkgconfig_2.0.3  
## [53] evaluate_0.14     lattice_0.20-38   labeling_0.3      htmlwidgets_1.5.1
## [57] cowplot_1.0.0     processx_3.4.2    tidyselect_1.1.0  plyr_1.8.6       
## [61] magrittr_1.5      R6_2.4.1          generics_0.0.2    DBI_1.1.0        
## [65] pillar_1.4.4      haven_2.3.1       foreign_0.8-75    withr_2.2.0      
## [69] mgcv_1.8-31       survival_3.1-8    abind_1.4-5       modelr_0.1.8     
## [73] crayon_1.3.4      car_3.0-8         utf8_1.1.4        rmarkdown_2.2    
## [77] viridis_0.5.1     grid_3.6.3        readxl_1.3.1      data.table_1.12.8
## [81] blob_1.2.1        callr_3.4.3       reprex_0.3.0      digest_0.6.25    
## [85] webshot_0.5.2     munsell_0.5.0     viridisLite_0.3.0